Abstract
We consider two formulations of a cellular automata: the first one uses a gather-update paradigm and the second one a collision-propagation paradigm. We show the equivalence of both descriptions and, using the latter paradigm, we propose a simple way to define a Cellular Automata on a graph with arbitrary topology. Finally, we exploit the duality of formulation to reconsider the problem of characterizing invertible cellular automata.
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Caiazzo, A., Falcone, J.-L., Chopard, B., Hoekstra, A.: Error investigations in complex automata models for reaction-diffusion systems. In: Umeo, H., et al. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 260–267. Springer, Heidelberg (2008)
Caldarelli, G.: Scale-Free Networks. Oxford University Press, Oxford (2007)
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)
Durand-Lose, J.: Representing reversible cellular automata with reversible block cellular automata. In: Discrete Mathematics and Theoretical Computer Sciences Proceedings AA (DM-CCG), pp. 145–154 (2001)
Hoekstra, A., Lorenz, E., Falcone, J.-L., Chopard, B.: Towards a complex automata formalism for multuscale modeling. Int. J. Multiscale Computational Engineering 5(6), 491–502 (2008)
Hoekstra, A.G., Falcone, J.-L., Caiazzo, A., Chopard, B.: Multi-scale modeling with cellular automata: The complex automata approach. In: Umeo, H., et al. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 192–199. Springer, Heidelberg (2008)
Marconi, S., Chopard, B.: Discrete physics, cellular automata and cryptography. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 617–626. Springer, Heidelberg (2006)
Razakanirina, R.M.: Cellular automata on graphs applied to financial flow simulation. Master’s thesis, University of Geneva, Computer Science department, Master thesis (2007)
Toffoli, T., Margolus, N.: Cellular Automata Machines: a New Environment for Modeling. MIT Press, Cambridge (1987)
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Chopard, B., Falcone, JL., Razakanirina, R., Hoekstra, A., Caiazzo, A. (2008). On the Collision-Propagation and Gather-Update Formulations of a Cellular Automata Rule. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_19
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DOI: https://doi.org/10.1007/978-3-540-79992-4_19
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